Download Geometry Proof Study Guide Geometry Proof Study Guide Page

Geometry Proof Study Guide
eName: ____________________________________________ Date: _______________ Block: _________
SHOW ALL WORK. Use another piece of paper as needed.
1.
Give an example of each of the following properties.
a. Reflexive Theorem of Angle Congruence
b. Symmetric Theorem of Angle Congruence
c. Transitive Theorem of Angle Congruence
2.
Use the diagram to determine if the statement is true or false.
a)
b)
c)
d)
e)
f)
g)
h)
3.
AD lies in plane N.
KD intersects plane N at point K.
AD  AJ
 IJL and  LJK are a linear pair.
 HJA and  LJH are supplementary.
 HJA and  LJH are complementary.
Plane M and plane O intersect at line r.
Line p and line q are parallel.
 AGD is a right angle and
AB , CD , and EF
intersect at point G.
a) m  CGB = ?
b) If m  FGC = 136o, then m  EGA = ?
c) If m  CGF = 138o, then m  EGD = ?
d) If m  EGA = 73o, then m  FGD = ?
4.
Solve the equation, writing a reason for each step:
13(2x – 3) – 20x = 3
Statements
Reasons
1) 13(2x – 3) – 20x = 3
1) Original equation
2) 26x – 39 – 20x = 3
2)______________________
3) 6x – 39 = 3
3)______________________
4) 6x = 42
4)______________________
5) x = 7
5)______________________
Geometry Proof Study Guide
5.
6.
Page 2
Complete the proof:
Given: Point K is in the interior of  LMN.
 LMN is a right angle.
Prove:  LMK and  KMN are complementary.
Statements
Reasons
1) _________________________
1)Given
2) _________________________
2)Definition of a right angle
3) _________________________
3) Given
4) _________________________
4)Angle addition postulate
5) _________________________
5) Substitution property of
equality
6) _________________________
6) Definition of
complementary angles.
Complete the proof:
Given:  1 and  2 form a linear pair; m  2 + m  3 + m  4 = 180o
Prove: m  1 = m  3 + m  4
Statements
Reasons
1)  1 and  2 form a linear pair;
 2 +  3 +  4 = 180o
1)________________________
2)  1 and  2 are supplementary
2)________________________
3) m  1 + m  2 = 180o
3)________________________
4) m  1 + m  2 = m  2 + m  3 + m  4
4)________________________
5) m  1 = m  3 + m  4
5)________________________
Geometry Proof Study Guide
7.
Page 3
Complete the proof:
Given: SU  LR ; TU  LN
Prove: ST  NR
Statements
Reasons
1) SU  LR ; TU  LN
1)________________________
2) SU = LR; TU = LN
2) ________________________
3) SU = ST + TU
3)________________________
LR = LN + NR
8.
4) ST + TU = LN + NR
4)________________________
5) ST + LN = LN + NR
5)________________________
6) ST + LN – LN = LN + NR - LN
6)________________________
7) ST = NR
7)________________________
8) ST  NR
8)________________________
Complete the proof:
Given: AB  DE ; B is the midpoint of AC ; E is the
midpoint of DF
Prove: BC  EF
Statements
Reasons
1) ________________________
1)Given
________________________
________________________
2) AB = DE
2) ________________________
3) ________________________
3) Definition of a midpoint
________________________
4) BC = DE
4)________________________
5) BC = EF
5)________________________
6) BC  EF
6)________________________
Geometry Proof Study Guide
Page 4
STUDY GUIDE ANSWERS
2.
a. True
e. True
LMN  LMN
If TUV  XYZ then XYZ  TUV .
b. False
f. False
If A  B and B  C , then
c. False
g. True
A  C .
d. True
h. False
90o
4.
Reasons:
46 o
2) Distributive property
138 o
3) Combine like terms (or Simplify)
o
17
4) Addition property of equality
5) Division property of equality
1.
a.
b.
c.
3.
a.
b.
c.
d.
5.
Statements:
1)  LMN is a right angle
2) m  LMN=90o
3) Point K is in the interior of  LMN
4) m  LMK + m  KMN = m  LMN
5) m  LMK + m  KMN = 90o
6)  LMK and  KMN are
complementary
6.
Reasons:
1) Given
2) Angles that form a linear pair are
supplementary (Linear pair
postulate)
3) Supplementary angles have a sum
of 180o (Definition of supplementary
angles)
4) Transitive property of equality
5) Subtraction property of equality
7.
Reasons:
1) Given
2) Congruent segments have equal
measures (Definition of congruent
segments)
3) Segment addition postulate
4) Transitive property of equality
5) Substitution property of equality
6) Subtraction property of equality
7) Simplify
8) Segments that have equal measures
are congruent (Definition of
congruent segments)
8.
Statements/Reasons:
1) AB  DE ; B is the midpoint of AC ;
E is the midpoint of DF
2) Segments are congruent have equal
measures (Definition of congruent
segments)
3) AB = BC; DE = EF
4) Transitive property of equality
5) Transitive property of equality
6) Segments that have equal measures
are congruent (Definition of
congruent segments)